Newform orbit 3783.1.g.j

• Label: 3783.1.g.j
• Level: $3783$
• Weight: $1$
• Character orbit: 3783.g
• Self dual: yes
• Analytic conductor: $1.888$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -3783
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3783 = 3 \cdot 13 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3783.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.88796294279\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{3}) \)
Defining polynomial:	\( x^{2} - 3 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{6}\)
Projective field:	Galois closure of 6.2.18046283229.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - \beta q^{2} + q^{3} + 2 q^{4} - \beta q^{6} + q^{7} - \beta q^{8} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 4 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3783\mathbb{Z}\right)^\times\).

\(n\)	\(781\)	\(1262\)	\(2329\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

3782.1

1.73205
−1.73205

−1.73205

1.00000

2.00000

0

−1.73205

1.00000

−1.73205

1.00000

0

3782.2

1.73205

1.00000

2.00000

0

1.73205

1.00000

1.73205

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3783.g	odd	2	1	CM by \(\Q(\sqrt{-3783}) \)
3.b	odd	2	1	inner
1261.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3783.1.g.j	yes	2
3.b	odd	2	1	inner	3783.1.g.j	yes	2
13.b	even	2	1		3783.1.g.i	✓	2
39.d	odd	2	1		3783.1.g.i	✓	2
97.b	even	2	1		3783.1.g.i	✓	2
291.c	odd	2	1		3783.1.g.i	✓	2
1261.c	even	2	1	inner	3783.1.g.j	yes	2
3783.g	odd	2	1	CM	3783.1.g.j	yes	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
3783.1.g.i	✓	2	13.b	even	2	1
3783.1.g.i	✓	2	39.d	odd	2	1
3783.1.g.i	✓	2	97.b	even	2	1
3783.1.g.i	✓	2	291.c	odd	2	1
3783.1.g.j	yes	2	1.a	even	1	1	trivial
3783.1.g.j	yes	2	3.b	odd	2	1	inner
3783.1.g.j	yes	2	1261.c	even	2	1	inner
3783.1.g.j	yes	2	3783.g	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(3783, [\chi])\):

\( T_{2}^{2} - 3 \)

\( T_{7} - 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - 3 \)
$3$	\( (T - 1)^{2} \)
$5$	\( T^{2} \)
$7$	\( (T - 1)^{2} \)
$11$	\( T^{2} - 3 \)